Question
Consider a cube with a volume of 64 cm3 . What can be concluded about the cube? Select the two that apply.(2 points) Responses The side length is 4 cm. The side length is 4 cm. The side length is 8 cm. The side length is 8 cm. Taking the cube root of its volume will determine its side length. Taking the cube root of its volume will determine its side length. The expression s2 , where s represents the side length was used to solve this problem.
Answers
GPT-4o mini
To analyze the cube with a volume of 64 cm³, we start by recalling that the volume \( V \) of a cube is given by the formula:
\[
V = s^3
\]
where \( s \) is the length of a side of the cube.
Given that the volume \( V = 64 \, \text{cm}^3 \):
\[
s^3 = 64
\]
To find the side length \( s \), we can take the cube root of both sides:
\[
s = \sqrt[3]{64} = 4 \, \text{cm}
\]
This means we can conclude the following:
1. **The side length is 4 cm.**
2. **Taking the cube root of its volume will determine its side length.**
So, the two correct conclusions are:
- **The side length is 4 cm.**
- **Taking the cube root of its volume will determine its side length.**
\[
V = s^3
\]
where \( s \) is the length of a side of the cube.
Given that the volume \( V = 64 \, \text{cm}^3 \):
\[
s^3 = 64
\]
To find the side length \( s \), we can take the cube root of both sides:
\[
s = \sqrt[3]{64} = 4 \, \text{cm}
\]
This means we can conclude the following:
1. **The side length is 4 cm.**
2. **Taking the cube root of its volume will determine its side length.**
So, the two correct conclusions are:
- **The side length is 4 cm.**
- **Taking the cube root of its volume will determine its side length.**